VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 56 



if a fixed point be assumed, viz. the centre of the tangent point for the index ; 

 then the beam compass being always opened to the computed length of the tan- 

 gent of the circle of divisions, it will be sufficiently near for cutting the divisions, 

 square to the circular arches between which they are placed. 



It will also be proper, to prevent unequal expansions, that the beam of the 

 compass should be formed of a piece of clean-grained white fir ; and that the 

 length between the points be inclosed in a tube of tin or brass ; without touching 

 the beam, except at the terminations, which will in a great measure protect it 

 from both alteration of moisture, and of heat from the body of the artist, during 

 the operation. It will be likewise proper to have a lever, or some equivalent con- 

 trivance, to bring the dividing plate forward ; that after lifting the little cylinders 

 out of the divisions, and resting them on the tops of the teeth, they may be 

 brought gently forward with an equal drag, and ultimately snap in between the 

 teeth, by the strength of the spring commanding the index ; by this means the 

 drag of the friction of the whole will be constantly the same way. 



Conclusion. — Now if, as it has been shown, a quadrant of any radius may be 

 read off to the 4000th part of an inch, then this quantity on a radius of the 3 

 feet will not be so much as 14- second ; and as the whole of the process is carried 

 on by contact, in which a greater error than that cf a 6o,OOOth part of an inch 

 cannot be admitted in any single operation, I should assuredly expect a 3-feet 

 quadrant, so divided, to be true in its divisions, and read off to at most 2 seconds. 

 But, after all, in an instrument like this, I should expect the greatest source of 

 error to be in the want of perfect coincidence of the centre of the divisions with 

 the actual centre on which the index revolves ; and therefore, that if, instead of 

 a quadrant of 3 feet radius, a complete circle of 5 feet diameter was divided, and 

 its divisions read oflf from the two opposite points, taking the mean, then the 

 errors of the centre will be wholly avoided. For this reason, I am very clearly of 

 opinion, that the sagacious proposition of Mr. Ramsden, to use circles instead of 

 quadrants, or other portions of circles, will bid much the fairest for perfection in 

 actual practice ; and that his ingenious method of making them both stiff and 

 light, by the use of hollow conical tubes by way of spokes, in the manner of a 

 common wheel, will enable him to mount them of 5 feet diameter, on hollow 

 axes, in the nature of a transit. By this means we shall have all the good pro- 

 perties of both the quadrant and transit united in one instrument ; and observa- 

 tions both of right ascension and declination, through the very same telescope, 

 as long since attempted by M. Roemer ; and to a degree of perfection and cer- 

 tainty, in point of declination, hitherto unattainable by the largest instruments 

 that have yet been made. 



N. B. In matters of very nice determination, small circumstances often come 

 to be of consequence ; and it is in this view that I mention what follows. It was 



